考虑交货期限的生产提前期的优化分析

Optimal Analysis of Lead Time Considering Due Date

针对交货期限和订单批量对生产提前期的影响问题,建立了多种类型订单成批达到的多服务台的排队模型,其中订单的批量服从泊松分布,加工时间服从负指数分布,并且不同类型产品的服务率是不同的.利用该系统对单阶段的装配或加工过程进行建模,应用马尔可夫过程的状态空间方法和全概率分解技术,得到了订单的平均生产提前期.进一步提出了一个多目标优化的问题,利用Goal Attainment Method对模型的参数进行优化,给出订单在生产线上最短生产提前期和最小加工成本的优化方案,利用生产提前期超过交货期限的概率来评价优化方案的优劣.最后,通过实例分析证明该模型的估计值是准确的.

Considering the problem of the influence of due date and batch arrivals on the lead time, a new queueing system based on the batch arrivals of multi-style orders for optimal design of single-stage assemblies was developed, in which the number of products belonging to an order was Poisson distributed and the servers had many styles with different service rates to different orders. Service time of manufacturing and assembly operations were exponentially distributed. By using the total probability decomposition technology and Markov process method, the average lead time was obtained. Then, a multi- objective optimal control problem was developed, in which the average lead time and the total operating costs of the system per period were minimized using Goal Attainment Method, and the approximate performance of the model was measured through employing the probability of average lead time over time constraints. Numerical examples show that the estimated values are accurate.